Fast and robust quantum computation with ionic Wigner crystals

TL;DR

This paper analyzes a quantum phase gate using Wigner crystals of ions in Penning traps, demonstrating that fast, robust two-qubit gates are feasible even without specific frequency conditions, and proposes a practical implementation method.

Contribution

It extends previous schemes by analyzing the case where the cyclotron and rotation frequencies differ, showing that fast, robust gates are still achievable and providing a realization method for the required dipole forces.

Findings

Two-qubit gates can be fast and robust without the condition w_c=2w_r.

The many-body Hamiltonian can be recast in canonical form despite magnetic field effects.

A practical realization of the state-dependent dipole forces is proposed.

Abstract

We present a detailed analysis of the modulated-carrier quantum phase gate implemented with Wigner crystals of ions confined in Penning traps. We elaborate on a recent scheme, proposed by two of the authors, to engineer two-body interactions between ions in such crystals. We analyze for the first time the situation in which the cyclotron (w_c) and the crystal rotation (w_r) frequencies do not fulfill the condition w_c=2w_r. It is shown that even in the presence of the magnetic field in the rotating frame the many-body (classical) Hamiltonian describing small oscillations from the ion equilibrium positions can be recast in canonical form. As a consequence, we are able to demonstrate that fast and robust two-qubit gates are achievable within the current experimental limitations. Moreover, we describe a realization of the state-dependent sign-changing dipole forces needed to realize the investigated quantum computing scheme.